there is somewhere an excess, which ought to be subtracted and referred to another class. Government cannot be divided into monarchical, aristocratic, and democratic; as there is a fourth class, the mixed. The old Division of the science of language into Grammar, Logic, and Rhetoric is redundant, as Logic is concerned with the laws of thought rather than of utterance, and therefore properly belongs to the science of mind.

4. The Co-ordinate Species into which a Genus is divided must be reciprocally exclusive; that is, no one of them must, in whole or in part, contain any other. In order to ascertain whether this rule, the propriety of which is obvious, has been complied with, Logicians apply the test of Dichotomy, to which any other Division, however complex, may be reduced. Thus, all the Co-ordinate Species, B, C, D, E, &c., of any Genus, A, may be represented under any one of the formulas, B and not-B; Cand not-C; D and not-D, &c. If the Dividing Members are mutually exclusive, C, D, and E will each be found under not-B; B, D, and E, under not-C; B, C, and E, under not-D; and so on. This rule is violated in a Cross Division, where, as we have already seen, the same individuals may appear under two or more of the Dividing Members: and also when a Member of a Subdivision is improperly co-ordinated with the Members of a primary Division. This last fault, however, is properly ranked under the next following rule. The ten Categories of Aristotle are now generally condemned as a faulty Division, because the last six of them are only subdivisions of the fourth, Relation. "For the Category where is the relation of a thing to other things in space; the category when is the relation of a thing to other things in time; action and passion constitute a single relation,—that of agent and patient"; &c.

5. A Division must proceed step by step, in regular

order, from proximate to remote differences, not overleaping any step which is properly intermediate. In other words, each Species, as it appears among the Dividing Members, must emerge directly from the Division of its own Proximate Genus. Divisio ne fiat per saltum veľ hiatum. Even the ordinary Division of all natural objects into animals, vegetables, and minerals is faulty in this respect, its three Species not being properly co-ordinate, as one step has been omitted. The primary Division should be by Dichotomy into organic and inorganic things, animals and vegetables appearing subsequently as a subdivision of the organic.

CHAPTER V.

THE DOCTRINE OF JUDGMENTS.

1. The Predicables and the Categories.-2. The Quantity, Quality, and Relation of Judgments according to the Aristotelical Doctrine.-3. The Hamiltonian Doctrine of Judgments.-4. The Explication of Propositions into Judgments.

UDGMENT is that act of mind whereby the rela

JUDG

tion of one Concept to another, or of an individual thing to a Concept, is determined, and, as a consequence of such determination, that two Concepts, or the individual thing and the Concept, are reduced to unity in Thought. A Judgment expressed in words is a Proposition, the two terms of the Judgment being called the Subject and Predicate of the Proposition. The assertions, iron is malleable, John is brave, determine a relation of agreement between the two terms involved in each, whereby these two are conceived as one, and thus expressed, malleable iron, brave John. On the other hand, the Judgment, quadrupeds are not rational, determines the relation of disagreement between the two Terms, so that one is now denied to be a Mark of the other, or, what is the same thing, the negative Mark, irrational, is now attached to the Concept, quadruped.

As we have already defined a Concept to be a representation of one or more objects through their distinctive Marks, it is evident that Judgment is the process through which Concepts are formed. In fact, to judge is to recognize a particular Mark or attribute as belonging, or not

'belonging, to a certain object or class of objects. The Judgment is not, strictly speaking, a comparison, but it is the mental act of conjoining or disjoining two things which results from a previous comparison of them with each other, and a consequent recognition of their agreement or disagreement. Hence, as Hamilton remarks, "every Concept is a Judgment fixed and ratified in a sign"; and, again, "a Concept may be viewed as an implicit or undeveloped Judgment; a Judgment as an explicit and developed Concept." Thus, the Concept man, which has the four Marks biped, two-handed, rational, animal, is the combined result of four separate Judgments which affirmed each of these attributes to be characteristic of man. Aristotle, the Father of Logic, seems to have regarded Judgments as the primary elements, out of which Concepts are formed; for his whole system is based upon an analysis of Judgments. Modern writers have preferred, as more convenient, and at least equally correct, the view which has here been taken, that Concepts are the elements of Judgments. In truth, each presupposes the other. If it be asked which, in the order of the mind's development, comes first, the answer is, neither; but a partial and confused apprehension of a thing, which is a young child's substitute for a Concept, and which is first cleared up by a succession of Judgments producing Concepts properly so called. Judgment is not arbitrary or dependent upon the will; I must, in Thought, affirm the union or the separation of the two Terms, according as the relation of agreement or disagreement is perceived to exist between them. Hence, the Judgment is always, at least subjectively, true; the Proposition, which is only the verbal affirmation, may be either true or false, according as it does, or does not, agree with the mental Judgment.

The mere succession or coexistence of two Thoughts in the mind does not constitute a Judgment. I may think

first of man, and then of animal; but no Judgment takes place until I affirm in Thought a perceived relation between them, until I think man is animal. Such a relation cannot be perceived between them unless one is regarded as an attribute or determination of the other; that is, one must be regarded as determining, and the other as determined. For if both were viewed as determining, there would be nothing determined; and both cannot be determined, unless there is something determining them. Hence there are three necessary parts of a Judgment; first, the Concept or thing determined, which is called the Subject; secondly, the determining or attributive notion, which is called the Predicate; and, thirdly, that which expresses the relation of determination between the Subject and the Predicate is called the Copula. The Subject and Predicate are called the Terms (termini) or Extremes of the Judgment; and the Copula may therefore be symbolized as a straight line connecting the two points which are its Terms or ends.

Though a Judgment necessarily consists of two Terms, it is nevertheless a single act of mind. There is a separate act of mind, whereby I perceive or conceive each of the two Terms taken separately; but it is only one act by which I perceive and affirm the relation between these two Terms, and thereby unite them into one process of Thought.

When the mental Judgment comes to be expressed in words as a Proposition, each of its three parts does not necessarily appear as a distinct word. The idiom of language often requires or enables us to express two, or even all three, of them by a single word; but, in accordance with the general Postulate of Logic, that we must be allowed to express all that is implicitly thought, we cannot deal logically with the Proposition until its form is so modified as to allow all the three elements to appear separately. Moreover, as has been already remarked, the Copula of a